The remarkable dexterity and versatility that the human arm exhibits in performing various tasks can be attributed largely to the kinematic redundancy of the arm, which provides the capability of reconfiguring the arm without affecting the hand position. A robotic manipulator is called (kinematically) "redundant" if it possesses more degrees of freedom (DOF) than is necessary for performing a specified task. Redundancy of a robotic manipulator is therefore determined relative to the particular task to be performed. For example, in the two-dimensional space, a planar robot with three joints is redundant for achieving any end-effector position; whereas the robot is non-redundant for tasks involving both position and orientation of the end-effector. In the three-dimensional space, a manipulator with seven or more joints is redundant because six degrees of freedom are sufficient to position and orient the end-effector in any desired configuration. In a non-redundant manipulator, a given position and orientation of the end-effector corresponds to a limited set of joint angles and associated robot configurations with distinct poses (such as elbow up or down). Therefore, for a prescribed end-effector trajectory and a given pose, the motion of the robot is uniquely determined. When this motion is undesirable due to collision with obstacles, approaching kinematic singularities, or reaching joint limits, there is no freedom to reconfigure the robot so as to reach around the obstacles, or avoid the singularities and joint limits.
Redundancy in the manipulator structure yields increased dexterity and versatility for performing a task due to the infinite number of joint motions which result in the same end-effector trajectory. However, this richness in choice of joint motions complicates the manipulator control problem considerably. In order to take full advantage of the capabilities of redundant manipulators, effective control schemes should be developed to utilize the redundancy in some useful manner. During recent years, redundant manipulators have been the subject of considerable research, and in the following references several methods have been suggested to resolve the redundancy:
1 D. E. Whitney, "Resolved motion rate control of manipulators and human prostheses," IEEE Trans. Man-Machine Syst., vol. MMS-10, no. 2, pp. 47-53, 1969. PA0 2. A. Liegeois, "Automatic supervisory control of the configuration and behavior of multibody mechanisms," IEEE Trans. System, Man Cybern., vol. SMC-7, no. 12, pp. 868-871, 1977. PA0 3. H. Hanafusa, T. Yoshikawa, and Y. Nakamura, "Analysis and control of articulated robot arms with redundancy," in Proc. 8th IFAC Triennial World Congress (Kyoto, Japan, 1981) pp. 1927-1932. PA0 4. T. Yoshikawa, "Analysis and control of robot manipulator with redundancy," in Proc. 1st Int. Symp. on Robotics Research (Bretton Woods, NH, 1983), pp. 735-747. PA0 5. Y. Nakamura and H. Hanafusa, "Task priority based redundancy control of robot manipulators," in Proc. 2nd Int. Symp. on Robotics Research (Kyoto, Japan, August 1984). PA0 6. T. Yoshikawa, "Manipulability and redundancy control of robotic mechanisms," in Proc. IEEE Int. Conf. on Robotics and Automation (St. Louis, Mo., March 1985), pp. 1004-1009. PA0 7. J. Baillieul, J. Hollerbach, and R. Brockett, "Programming and control of kinematically redundant manipulators," in Proc. 23rd IEEE Conf. on Decision and Control, pp. 768-774, December 1984. PA0 8. J. Baillieul, "Kinematic programming alternatives for redundant manipulators," in Proc. IEEE Int. Conf. on Robotics and Automation (St. Louis, Mo., March 1985), pp. 772-728. PA0 9. --------, "Avoiding obstacles and resolving kinematic redundancy," in Proc. IEEE Int. Conf. on Robotics and Automation (San Francisco, Calif., April 1986), pp. 1698-1704. PA0 10. J. Baillieul, R. Brockett, J. Hollerbach, D. Martin, R. Percy, and R. Thomas, "Kinematically redundant robot manipulators," in Proc. NASA Workshop on Space Telerobotics (Pasadena, Calif.,), vol. 2, pp. 245-255, January 1987. PA0 11. J. Baillieul, "Design of kinematically redundant mechanisms," in Proc. 24th IEEE Conf. on Decision and Control (Ft. Lauderdale, Fla., December 1985), pp. 18-21. PA0 12. I. D. Walker and S. I. Marcus, "An approach to the control of kinematically redundant robot manipulators," in Proc. American Control Conf. (Seattle, Wash., June 1986), pp. 1907-1912. PA0 13. C. A. Klein and C. H. Huang, "Review of pseudoinverse control for use with kinematically redundant manipulators," IEEE Trans. System, Man Cybern., vol. SMC-13, no. 3, pp. 245-250, 1983. PA0 14. S. Y. Oh, D. Orin, and M. Bach, "An inverse kinematic solution for kinematically redundant robot manipulators," J. Robotic Syst., vol. 1, no. 3, pp. 235-249, 1984. PA0 15. S. Y. Oh, "Inverse kinematic control for redundant manipulators," in Proc. IEEE Workshop on Intelligent Control (Troy, N.Y., 1985), pp. 53-57. PA0 16. O. Khatib, "A unified approach for motion and force control of robot manipulators: The operational space formulation," IEEE J. Robotics Automat., vol. RA-3, no. 1, pp. 43-53, 1987. PA0 17. C. A. Klein, "Use of redundancy in the design of robotic systems," in Proc. 2nd Int. Symp. on Robotics Research (Kyoto, Japan, August 1984). PA0 18. A. A. Maciejewski and C. A. Klein, "Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments," Int. J. Robotics Res., vol. 4, no. 3, pp. 109-117. 1985. PA0 19. C. A Klein and A. I. Chirco, "Dynamic simulation of a kinematically redundant manipulator system," J. Robotic Syst., vol. 4, no. 1, pp. 5-23, 1987. PA0 20. D. R. Baker and C. W. Wampler, "Some facts concerning the inverse kinematics of redundant manipulators," in Proc. IEEE Int. Conf. on Robotics and Automation (Raleigh, N.C., March 1987). pp. 604-609. PA0 21. J. M. Hollerbach, "Optimum kinematic design for a seven degree of freedom manipulator," in Proc. 2nd Int. Symp. on Robotics Research (Kyoto, Japan, August 1984). PA0 22. J. M. Hollerbach and K. C. Suh, "Redundancy resolution of manipulators through torque optimization," in Proc. IEEE Int. Conf. on Robotics and Automation (St. Louis, Mo., March 1985), pp. 1016-1021. PA0 23. O. Egeland, "Cartesian control of a hydraulic redundant manipulator," in Proc. IEEE Int. Conf. on Robotics and Automation (Raleigh, N.C., April 1987), pp. 2081-2086. PA0 24. L. Sciavicco and B. Siciliano, "A dynamic solution to the inverse kinematic problem for redundant manipulators," in Proc. IEEE Int. Conf. on Robotics and Automation (Raleigh, N.C., April 1987), pp. 1081-1087. PA0 25. P. Hsu, J. hauser, and S. Sastry, "Dynamic control of redundant manipulators," in Proc. IEEE Int. Conf. on Robotics and Automation (Philadelphia, Pa., April 1988), pp. 183-187. PA0 26. R. V. Dubey, J. A. Euler, and S. M. Babcock, "An efficient gradient projection optimization scheme for a 7 dof redundant robot with spherical wrist," in Proc. IEEE Int. Conf. on Robotics and Automation (Philadelphia, Pa., April 1988), pp. 28-36.
Whitney [1]suggests the use of Jacobian pseudoinverse for the control of redundant manipulators. Liegeois [2]proposes a modification to the pseudoinverse approach to resolve manipulator redundancy. Nakamura and Yoshikawa [3]-[6] develop a scheme based on task priority using pseudoinverses. Baillieul [7]-[11] proposes the extended Jacobian method to minimize or maximize an objective function. Walker and Marcus [12] suggest a method based on the pseudoinverse approach to impose a constraint relationship on the manipulator. A comprehensive review of the pseudoinverse approach to redundant manipulators is given by Klein and Huang [13]. Oh, Orin, and Bach [14], [15] describe a numerical procedure for solving the inverse kinematic problem which uses constraints on the manipulator. Khatib [16] gives a method for the resolution of redundancy using the robot dynamics in the operational space. Klein [17]-[19] addresses obstacle avoidance and dynamic simulation of redundant robots. Baker and Wampler [20] study the kinematic properties of redundant manipulators. The problems of robot design and torque optimization are addressed by Hollerbach [21], [22]. Egeland [23] describes a method for Cartesian control of a hydraulic redundant manipulator. Sciavicco and Siciliano [24] give dynamic solution to the inverse kinematic problem for redundant robots. Hsu, Hauser, and Sastry [25] discuss the resolution of redundancy using the manipulator dynamics. Dubey, Euler, and Babcock [26] describe a gradient projection optimization scheme for 7-DOF robots.
Over the past two decades, investigations of redundant manipulators have often been explicitly or implicitly based on the Jacobian pseudoinverse approach for the utilization of redundancy through local optimization of some objective function. Furthermore, most proposed methods resolve the redundancy in joint space and are concerned solely with solving the inverse kinematic problem for redundant manipulators.
U.S. Pat. No. 4,860,215 issued Aug. 22, 1988 to the inventor herein, discloses related subject matter and background prior art. U.S. Pat. Nos. 4,685,054; 4,621,332; 4,794,547; and 4,641,251 also disclose relevant, but distinguishable subject matter.